When the beams of three lasers are directed through a suitable medium; they combine to form a nonlinear polarization at all possible frequency combinations, .omega..sub.4 = .+-..omega..sub.1 .+-..omega..sub.2 .+-..omega..sub.3 ; and coherent radiation at frequency .omega..sub.4 is in turn generated by the nonlinear polarization. As the induced polarization wave passes through the medium, it travels in a manner governed by the vector sum of the wave numbers of the three beams, or (K.sub.1 + K.sub.2 + K.sub.3). This vector sum, in general, is not equal to the vector wave number K.sub.4 of the generated radiation (since propagation is frequently dependent). Since the generating wave and the generated wave travel with different velocities and directions, the radiation produced in different parts of the medium will not be in phase, and destructive interference will reduce the amount of generated radiation emitting from the conversion medium. The condition for constructive addition of the output from different portions of the medium is EQU K.sub.1 + K.sub.2 + K.sub.3 = K.sub.4
or, for the collinear propagation, EQU (.omega..sub.1 n.sub.1 /c) + (.omega..sub.2 n.sub.2 /c) + (107 .sub.3 n.sub.3 /c) + (.omega..sub.4 n.sub.4 /c),
where n.sub.i is the index of refraction of the medium for frequency .omega..sub.i. The problem of satisfying the latter equation is known as the phase-matching problem. In the prior art, the frequencies involved in this equation have generally been held fixed, while attempts were made to satisfy the equation by changing the indices of refraction.
In gaseous media, for example, the standard approach has been to add a gas, the frequency dependence of which is opposite to that of the conversion medium. See, for example, U.S. Pat. No. 3,795,819, issued to S. E. Harris on Mar. 5, 1974. By appropriate choice of the mixture, the index of refraction can be adjusted to match the speed of the generating and generated waves. This technique suffers from a number of practical problems. Notably, it is very difficult to achieve the correct proportions over a substantial length and, typically, only a small fraction of the conversion medium will have the correct ratio of components and will contribute to the coversion. In the case of crystalline conversion media, the temperature is sometimes varied in order to change the index. See, for example, the article by F. Zernike, Physical Review Letters, Vol. 22, No. 931 (1969). Another method involves the recognition that appropriate indices of refraction may be found near the anomalous dispersion produced by a resonance. This was suggested by Armstrong et al in their article in Physical Review, Vol. 127, No. 20, page 1183 (1962) and was demonstrated in solids in 1969 by Zernike as previously stated. This prior art was unable to achieve resonance enhancement and phase matching simultaneously.
Typically, the prior art (see, for example, U.S. Pat. No. 3,914,618, issued to S. E. Harris on Oct. 21, 1975) increased the strength of the output signal by the use of a two-photon resonant enhancement of the nonlinear susceptibility, wherein the sum or difference of two of the input frequencies is made equal to .OMEGA., the equivalent frequency of a transition which requires the emission or absorption of two photons. See FIG. 2, showing a typical prior art level diagram. Only two lasers were used, one adjusted to a frequency .omega..sub.1 .apprxeq. .OMEGA./2 and a second one adjusted to a frequency .omega..sub.2. The output frequency .omega..sub.3 is then equal to 2.omega..sub.1 .+-. .omega..sub.2, where two phontons from laser 1 and one photon from laser 2 combined to form the output. The fact that 2.omega..sub.1 is close to .OMEGA. results in resonance enhancement of this particular combination out of the possible combinations of the two lasers (2.omega..sub.1 .+-. .omega..sub.2, 2.omega..sub.2 .+-. .omega..sub.1, etc.), which in turn results in a strong signal. Absent a phase-matching gas the output frequency is not phase-matched and only a portion of the conversion medium contributes to providing an output. The first Harris U.S. Pat. No. 3,795,819 discloses the use of three lasers, but teaches no difference between a threelaser apparatus and a two-laser apparatus.
One method in the prior art takes advantage of a pecularity that results when there is available a closely spaced doublet line. See, for example, U.S. Pat. Nos. 3,816,744 and 3,892,979 issued to R. T. Hodgson on June 11, 1974 and July 1, 1975, respectively. There, the two-photon resonance .OMEGA. is reached by one laser, but not directly. Instead of having 2.omega..sub.1 = .OMEGA., .omega..sub.1 is adjusted to a higher frequency than .OMEGA., as indicated in the energy level diagram of FIG. 4, so that the photon of frequency .omega..sub.1 has an energy between the energy levels at a closely-spaced doublet, which frequency .omega..sub.1 usually lies in the ultraviolet portion of the spectrum. Stimulated Raman scattering produces a photon the frequency of which is equal to the difference between .omega..sub.1 and the two-photon resonance .OMEGA.. .OMEGA. then equals .omega..sub.1 - .omega..sub.2, not 2.omega..sub.1 as in the prior art illustrated in FIG. 2. The output at a frequency of .omega..sub.4 is formed by adding the output frequency .omega..sub.3 from a second laser, .omega..sub.4 = .omega..sub.3 + .OMEGA. = .omega..sub.3 + .omega..sub.1 + .omega..sub.2.
Between the two resonances of the doublet, the dispersion and hence the index changes very rapidly. It is possible, therefore, to produce a compromise between the frequency for optimum production of the stimulated Raman scattering (which is necessary to reach the two photon resonance .OMEGA.), and between the frequency for optimum phase matching, The frequency range over which this method applies is fairly broad, but it does not begin to cover the entire spectrum. Limitations of this method are that it is difficult to produce .omega..sub.1 efficiently for use in generating the higher ultraviolet because .omega..sub.1 must be greater then .OMEGA.; the frequency chosen must be a compromise between production of the Raman process and phase matching; for broader tunability, a phase-matching gas is required, with the consequent disadvantages discussed above; and the region between the two resonances of the doublet is one where the contribution from each resonance to the nonlinear susceptability is equal and opposite, with the result that the resonance enhancement is therefore substantially reduced, giving a low output level.